theorem
proved
framework_self_consistent
show as:
view math explainer →
open explainer
Read the cached plain-language explainer.
open lean source
IndisputableMonolith.Foundation.SpectralEmergence on GitHub at line 543.
browse module
All declarations in this module, on Recognition.
explainer page
depends on
formal source
540
541 Input (construction): D = 3, V = 2^D = 8, gen = face_pairs = 3
542 Output (spectral): D = 3, V = 8, gen = 3 (from this module) -/
543theorem framework_self_consistent :
544 SelfConsistent 3 3 8 (V 3) 3 (face_pairs 3) :=
545 ⟨rfl, Q3_vertices.symm, three_generations.symm⟩
546
547/-- **THEOREM (Numerological Summary)**: The key numbers of the Standard
548 Model are all cube numbers:
549
550 8 = 2³ (vertices = states per octave)
551 12 = 3 × 2² (edges = gauge generators)
552 6 = 3 × 2 (faces = face pairs × 2)
553 3 (face pairs = generations = colors = charges)
554 48 = 2³ × 3! (automorphisms = total fermion states)
555 24 = 3 × 8 (fermion flavors = D × V)
556 1 (consciousness ground state = unique minimum)
557
558 All from D = 3. Zero parameters. -/
559theorem numerological_summary :
560 V 3 = 8 ∧
561 E 3 = 12 ∧
562 F₂ 3 = 6 ∧
563 face_pairs 3 = 3 ∧
564 aut_order 3 = 48 ∧
565 fermion_flavors = 24 ∧
566 consciousness_ground.is_zero_defect :=
567 ⟨Q3_vertices, Q3_edges, Q3_faces, three_generations,
568 Q3_aut_order, fermion_count_24, consciousness_is_zero_defect⟩
569
570end
571
572end SpectralEmergence
573end Foundation